1. Heat the oven to 325 degrees. Using about half the butter, generously butter a large gratin dish or baking dish (9- to 10-by-13- to 14-inch).

2. Washing and trimming the celery: Tear the celery stalks from the head. You should have about 10 or 12 sturdy outer stalks. Stop tearing off the stalks when you reach the shorter, pale, tender stalks, or the heart. Set it aside. Rinse the celery stalks, giving special attention to the inside of the base of each stalk, where dirt tends to lodge. You may need a vegetable scrubber to remove stubborn dirt. Trim off the top part of the stalk where it branches into leaves, and set the tops aside with the heart. Using a small paring knife or vegetable peeler, scrape the outside of each celery stalk to remove the fibrous strings that run its length. Cut the stalks into 3- to 4-inch lengths. Arrange them in a layer in the baking dish. It's fine if the sticks overlap some; they will shrink and flatten into a single layer as they braise.

3. The aromatics: Finely chop the reserved celery heart, with the celery tops and leaves. Melt the remaining butter in a medium skillet (IO-inch) over medium-high heat. Add the shallot, thyme, and chopped celery heart and leaves. Season with salt and pepper. Saute, stirring occasionally, until the vegetables are soft and beginning to brown, about 10 minutes. Pour in the wine and simmer until the pan is almost dry, about 3 minutes. Add the stock and simmer until reduced by half, another 6 minutes or so.

4. The braise: Pour the celery-shallot-stock mixture over the celery sticks. Cover with foil and slide into the middle of the oven to braise until the celery has collapsed and feels very tender when prodded with a knife tip, about I hour and 15 minutes.

5. The finish: Remove the celery from the oven, and increase the oven heat to 400 degrees. Sprinkle the cheese and bread crumbs over the celery, and return to the oven until the cheese is melted and the top is crusty and browned, about 10 more minutes. Serve hot
or warm.